ME GATE 2012 - Online Test
Q1. A concentrated mass m is attached at the centre of a rod of length 2L as shown in the figure. The
rod is kept in a horizontal equilibrium position by a spring of stiffness k. For very small amplitude
of vibration, neglecting the weights of the rod and spring, the undamped natural frequency of the
system is
Answer : Option D
Explaination / Solution:
No Explaination.
Q2. Consider two infinitely long thin concentric tubes of circular cross section as shown in the figure.
If D1 and D2 are the diameters of the inner and outer tubes respectively, then the view factor F22 is given by
Answer : Option D
Explaination / Solution:
No Explaination.
Q3. The homogeneous state of stress for a metal part undergoing plastic deformation is
Where the stress component values are in MPa. Using von Mises yield criterion, the value of
estimated shear yield stress, in MPa is
Answer : Option B
Explaination / Solution:
No Explaination.
Q4. A force of 400 N is applied to the brake drum of 0.5 m diameter in a band-brake system as shown
in the figure, where the wrapping angle is 180°. If the coefficient of friction between the drum
and the band is 0.25, the braking torque applied, in N.m is
Answer : Option B
Explaination / Solution:
No Explaination.
Q5. A solid circular shaft needs to be designed to transmit a torque of 50 N.m. If the allowable shear
stress of the material is 140 MPa, assuming a factor of safety of 2, the minimum allowable design
diameter in mm is
Answer : Option B
Explaination / Solution:
No Explaination.
Q6. Two steel truss members, AC and BC, each having cross sectional area of 100 mm2, are
subjected to a horizontal force F as shown in figure. All the joints are hinged
. If F = 1 kN, the magnitude of the vertical reaction force developed at the point B in kN is
Answer : Option A
Explaination / Solution:
No Explaination.
Q7. Two steel truss members, AC and BC, each having cross sectional area of 100 mm2, are subjected to a horizontal force F as shown in figure. All the joints are hinged
The maximum force F in kN that can be applied at C such that the axial stress in any of the truss
members DOES NOT exceed 100 MPa is
Answer : Option B
Explaination / Solution:
No Explaination.
Q8. For a particular project, eight activities are to be carried out. Their relationships with other
activities and expected durations are mentioned in the table below. 
The critical path for the project is
Answer : Option C
Explaination / Solution:
Critical path for the project is
a - d - f - h
Total time = 18 days.
Q9. For a particular project, eight activities are to be carried out. Their relationships with other
activities and expected durations are mentioned in the table below.
If the duration of activity f alone is changed from 9 to 10 days, then the
Answer : Option A
Explaination / Solution:
Critical path remains same and total duration will increase by 1 day and it takes 19 days to
complete.
Q10. The cost function for a product in a firm is given by 5 q2, where q is the amount of production.
The firm can sell the product at a market price of Rs 50 per unit. The number of units to be
produced by the firm such that the profit is maximized is
Answer : Option A
Explaination / Solution:
No Explaination.
